Relations and Functions — Class 11 solved problems

26 problems from this chapter, each solved step by step.

Let S= N 0. Define a relation R from S to R by: R= (x, y): log_e y = x log_e ((x)/(5)), x S, y R. Then, the sum of all the elements in the range of R is equal t
The sum of all the elements in the range of R is infinite.
Find the number of all one-one functions from set A=1,2,3 to itself.
The number of all one-one functions from set A=1,2,3 to itself is 6.
If the domain of the function f(x) = (1)/(√(10 + 3x - x²)) + (1)/(√(x + |x|)) is (a, b), then (1 + a)² + b² is equal to:
26
If the domain of the function log_5(18x-x²-77) is (α, β) and the domain of the function log_(α-1)((2x²+3x-2)/(x²-3x-4)) is (,), then α²+β²+ ² is equal to:
171
The function f is defined by f(x)= 1-x, & x<0 1, & x=0 x+1, & x>0 Draw the graph of f(x).
The graph of f(x) consists of three parts: a line y=1-x for x<0, a point (0,1) for x=0, and a line y=x+1 for x>0. All three parts connect at the point (0,1).
Let f be a function such that f(x) + 3 f (24/x) = 4x, x 0. Then f(3) + f(8) is equal to:
11
Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not? (i) R=(2,1),(3,1),(4,2), (ii) R=(2,2
(i) is a function. (ii) is not a function. (iii) is a function.
If P=a, b, c and Q=r, form the sets P × Q and Q × P. Are these two products equal?
The sets are P × Q = (a, r), (b, r), (c, r) and Q × P = (r, a), (r, b), (r, c). These two products are not equal.
If A × B=(p, q),(p, r),(m, q),(m, r), find A and B.
A = p, m and B = q, r
If R is the set of all real numbers, what do the cartesian products R × R and R × R × R represent?
The Cartesian product R × R represents the two-dimensional Cartesian coordinate plane, and R × R × R represents the three-dimensional Cartesian coordinate space
Find the domain of the function f(x)=(x²+3 x+5)/(x²-5 x+4)
The domain of the function is all real numbers except 1 and 4, which can be written as R 1, 4.
If (x+1, y-2)=(3,1), find the values of x and y.
The values are x=2 and y=3.
Let A=1,2,3,4,5,6. Define a relation R from A to A by R=(x, y): y=x+1 (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codomain and
The relation R = (1,2), (2,3), (3,4), (4,5), (5,6). Domain (R) = 1,2,3,4,5. Codomain (R) = 1,2,3,4,5,6. Range (R) = 2,3,4,5,6.
If the range of the function f(x) = (5 - x)/(x² - 3x + 2), x ≠ 1,2, is ( -∞, α) [β, ∞), then α² + β² is equal to:
194
If the domain of the function f(x)=log_7 (1-log_4(x²-9x+18)) is (α,β) (,), then α+β+ + is equal to:
18
Define the function f: R → R by y=f(x)=x², x R. Complete the Table given below by using this definition. What is the domain and range of this function? Draw the
The completed table is: |l|l|l|l|l|l|l|l|l|l| x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 y=f(x)=x² & 16 & 9 & 4 & 1 & 0 & 1 & 4 & 9 & 16. The domain of the funct
Let N be the set of natural numbers. Define a real valued function f: N → N by f(x)=2 x+1. Using this definition, complete the table given below. |r|c|c|c|c|c|c
The completed table is: |r|c|c|c|c|c|c|c| x & 1 & 2 & 3 & 4 & 5 & 6 & 7 y & f(1)=3 & f(2)=5 & f(3)=7 & f(4)=9 & f(5)=11 & f(6)=13 & f(7)=15
If P=1,2, form the set P × P × P.
P × P × P = (1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)
Let f(x)=x² and g(x)=2 x+1 be two real functions. Find (f+g)(x),(f-g)(x),(f g)(x),((f)/(g))(x).
(f+g)(x) = x² + 2x + 1, (f-g)(x) = x² - 2x - 1, (fg)(x) = 2x³ + x², ((f)/(g))(x) = (x²)/(2x+1) for x ≠ -(1)/(2).
Let f: R → R be a function defined by f(x) = (2 + 3a) x² + ( (a + 2)/(a - 1)) x + b, a ≠ 1. If f(x + y) = f(x) + f(y) + 1 - (2)/(7) xy, then the value of 28 Σ_i
667
Let A be the set of all 50 students of Class X in a school. Let f: A → N be function defined by f(x)= roll number of the student x. Show that f is one-one but n
The function f is one-one but not onto.
Let f(x)=√x and g(x)=x be two functions defined over the set of nonnegative real numbers. Find (f+g)(x),(f-g)(x),(f g)(x) and ((f)/(g))(x).
(f+g)(x) = √x + x (f-g)(x) = √x - x (fg)(x) = x³/2 ((f)/(g))(x) = (1)/(√x)
Let R be the set of real numbers. Define the real function f: R → R by f(x)=x+10 and sketch the graph of this function.
The graph of the function f(x) = x+10 is a straight line passing through the points (-10, 0) and (0, 10).
Let f=(1,1),(2,3),(0,-1),(-1,-3) be a linear function from Z into Z. Find f(x).
f(x) = 2x - 1
Let A=1,2 and B=3,4. Find the number of relations from A to B.
The number of relations from A to B is 16.
Define the real valued function f: R-0 → R defined by f(x)=(1)/(x), x R-0. Complete the Table given below using this definition. What is the domain and range of
The completed table is: |l|c|c|c|c|c|c|c|c|c| x & -2 & -1.5 & -1 & -0.5 & 0.25 & 0.5 & 1 & 1.5 & 2 y=(1)/(x) & -0.5 & -0.67 & -1 & -2 & 4 & 2 & 1 & 0.67 & 0.5 T

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